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〈a, b | aab=ba, bbb=aaa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a5 ⇒ a4
  2. a4b ⇒ a3b
  3. ba ⇒ a2b
  4. b3 ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2aa4ba3b2a2b2a3
11aba2bab2a3ba2b2aa4ba3b2a2b2a3
aaa2ba2a3ba3b2a3a4ba3b2a3a4ba3b2a3b2a3
bbbab2ba2b2aa3ba3b2a2a4ba3b2a3a4a4
a2a2a3ba3a4ba3b2a3a4ba3b2a3a4ba3b2a3b2a3
bababa2b2a2ba3b2a3a4ba3b2a3a4ba3b2a3a4a4
b2b2b2aa3b2a2a4ba3b2a3a4ba3b2a3a4ba3ba3
a3a3a4ba3a4ba3b2a3a4ba3b2a3a4ba3b2a3b2a3
ba2ba2ba3b2a3ba3b2a3a4ba3b2a3a4ba3b2a3a4a4
b2ab2ab2a2a4b2a3a4ba3b2a3a4ba3b2a3a4ba3ba3
a4a4a4ba3a4ba3b2a3a4ba3b2a3a4ba3b2a3b2a3
ba3ba3ba3b2a3ba3b2a3a4ba3b2a3a4ba3b2a3a4a4
b2a2b2a2b2a3a4b2a3a4ba3b2a3a4ba3b2a3a4ba3ba3
b2a3b2a3b2a3a4b2a3a4ba3b2a3a4ba3b2a3a4ba3ba3

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

33 unique, 303 total

Length:Presentation:Description:Related:
9 〈a, b | aaaa=b, abbb=1〉 Isomorphic to ℤ13 189 isomorphic
9 〈a, b | aba=b, baab=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
10 〈a, b | aaaa=b, abbb=a〉 Finite commutative monoid with 13 elements 10 isomorphic
10 〈a, b | aaaa=b, abbb=b〉 Finite commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaab=b, abba=a〉 Finite non-commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aaa=ab, babb=b〉 Finite non-commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaa=ab, bba=bb〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=ab, bbb=ab〉 Finite non-commutative monoid with 13 elements 1 isomorphic
10 〈a, b | aaa=ab, bbb=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=bb, aab=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=b, abbbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aab=b, abbba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
10 〈a, b | bb=aa, aaab=ba〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=aa, bbbb=a〉 Finite commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=ab, bbbb=a〉 Finite commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaab=bb, bbbb=a〉 Finite commutative monoid with 13 elements 14 isomorphic
11 〈a, b | aaab=b, aabba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaba=b, babbb=a〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=bb, aabbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=ab, abbb=bb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, abbb=ba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, babb=ab〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=ab, bbbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbbb=aa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aba=bb, abbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ab, bbb=aaa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=a, bbbbbb=a〉 Finite commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=b, ababba=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=a, baaa=bbb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbb=bba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | ab=aa, aaaa=bbb〉 Finite non-commutative monoid with 13 elements 7 isomorphic
11 〈a, b | ab=aa, baaa=bbb〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | ab=a, baaaaaa=b〉 Finite non-commutative monoid with 13 elements